Question: $\dfrac{ -10k + l }{ -4 } = \dfrac{ -10k + 4m }{ 7 }$ Solve for $k$.
Answer: Multiply both sides by the left denominator. $\dfrac{ -10k + l }{ -{4} } = \dfrac{ -10k + 4m }{ 7 }$ $-{4} \cdot \dfrac{ -10k + l }{ -{4} } = -{4} \cdot \dfrac{ -10k + 4m }{ 7 }$ $-10k + l = -{4} \cdot \dfrac { -10k + 4m }{ 7 }$ Multiply both sides by the right denominator. $-10k + l = -4 \cdot \dfrac{ -10k + 4m }{ {7} }$ ${7} \cdot \left( -10k + l \right) = {7} \cdot -4 \cdot \dfrac{ -10k + 4m }{ {7} }$ ${7} \cdot \left( -10k + l \right) = -4 \cdot \left( -10k + 4m \right)$ Distribute both sides ${7} \cdot \left( -10k + l \right) = -{4} \cdot \left( -10k + 4m \right)$ $-{70}k + {7}l = {40}k - {16}m$ Combine $k$ terms on the left. $-{70k} + 7l = {40k} - 16m$ $-{110k} + 7l = -16m$ Move the $l$ term to the right. $-110k + {7l} = -16m$ $-110k = -16m - {7l}$ Isolate $k$ by dividing both sides by its coefficient. $-{110}k = -16m - 7l$ $k = \dfrac{ -16m - 7l }{ -{110} }$ Swap signs so the denominator isn't negative. $k = \dfrac{ {16}m + {7}l }{ {110} }$